Analytic Model for Non-Steady State Heat Transfer of Powder …engineering.snu.ac.kr/pdf/2005(22)/2005_CHJ_Analytic... · 2014-07-29 · Keywords: Hot pressing roller, Heat transfer,

Materials Science Forum Vols. 475-479 (2005) pp. 3227-3230 online at http://www.scientific.net © 2005 Trans Tech Publications, Switzerland

Analytic Model for Non-Steady State Heat Transfer of Powder Pressing Roller

H.-J. Chang1·a, H. N. Han2·b, M. W. Moon1·c, K.-H Lee3.d and K. H. Oh1

'6

1 School of Materials Science and Engineering, Seoul National University, Seoul, Korea 151-742

2 Materials Processing Department, Korea Institute of Machinery & Materials, 66, Sangnam-dong,

Changwon, Kyungnam, Korea 641-010

3 POSCO, Pohang, Gyeongbuk, 790-785 Korea

"[email protected], [email protected], [email protected], [email protected], 6 [email protected]

Keywords: Hot pressing roller, Heat transfer, Analytic solution, FEM

Abstract. An analysis for non steady state heat transfer of a hot pressing roller was suggested in !­

dimensional model. The surface temperature on hot pressing roller was predicted by using surface

contact heat transfer coefficient calculated with induced analytic solution. We calculated the size of

iron powder, influencing on surface contact heat transfer coefficient. Since coarse iron powder has

reduced heat transfer coefficient during contacting on roll surface with smaller contact area,

temperature on roller surface has been expected to decrease. This predicted temperature by the

analytic model was fairly reasonable in comparison with experimental data and finite element

model.

Introduction

A hot roll pressing system is often utilized for agglomerating hot particulate matters because of

conceptual simplicity and an economical operation cost. For a successful operation of a roll

compaction, there have been many studies on rolling parameters [1-3]. A main focus of these

studies is a final product not a roller. However, a thermal behavior of the roller during hot pressing

is very closely related with a lifetime of the roller, and fmally affects the production efficiency. To

obtain appropriate operating conditions of the hot roll pressing, it is necessary to analyze the

thermal behavior of the roller. In this study, an analytic model, which can calculate non steady state

heat transfer of the hot pressing roller, was suggested. The accuracy of the analytic model was

verified with a finite element method (FEM) and experimental results.

Mathematical method

The hot pressing roller with a spiral type cooling system is illustrated in Fig I. Here, ro and rs

indicate the distance from a roll center to a cooling pipe and a total radius of the roller, respectively.

The analytic solution for non steady state heat transfer of the roller is solved in spherical coordinate

3228 PRICM-5

to simplify the calculation system. For the purpose of reducing the error due to the coordinate

change, a correction factor was introduced in a heat transfer coefficient.

A governing equation and boundary conditions of heat transfer at the spherical coordinate are

given by

aT 1 a2 (rT) -=a----at r 8r 2 r =r. dT =H (T-T)

dr c c

r =rs dT { -Hs(T-TP) -=f(t)= dr 0

(1)

t=O

where Tc, T P• t; and tr are temperature of cooling water, powder temperature, contact time between

hot powder and a roller among a time period and total time period for 1 revolution, respectively. He, Hs and a. are the effective heat transfer coefficients and thermal diffusivity, respectively. The

subscripts C and S indicate cooling pipe and surface. They are expressed by following form

H =he c k '

H = Fchs s k '

(2)

where k, Cp. p and Fe are conductivity, specific heat, density of the roller and a correction factor,

respectively. he. and hs are the heat transfer coefficient between cooling pipe and roller and the one

between roller and powders, respectively. They could be calculated by the well-known equation [4]

and the Holm tube model proposed by Degiovanni et a/.[5], respectively.

(3)

where D, Pw. Uw, flw, Cp,w and kw are the effective diameter of a cooling pipe, density, velocity,

viscosity, specific heat and thermal conductivity of cooling water, respectively. kh, a and b are

harmonic mean of thermal conductivity between two contact matters, a mean radius and a contact

radius of powder particles, respectively [6] . Physical meaning of the correction factor are briefly

explained that the correction factor may drop down an over estimated surface area. The solution of

Eq. (1) was derived by Duhamel equation [7], which was given by

1 T(r,t) = -U(r- r0,t)

r

(4)

Materials Science Forum Vols. 475-479 3229

where U, x and L are variables written by U = r ( T- Tc ), x = r- r0 and L = r5 - r0 , respectively.

Experiment and FEM modeling

The roll pressing with roll speed of 5rpm was carried out to measure the temperature at a roll

surface using an IR camera. SKT4 steel was used as a material of the roller. Two kinds of iron

powder, course powder named as PM1 and fine powder named as PM2, were used in the roll

compaction. tr and t; were 12sec and 1.5sec, respectively. Sizes and properties of the roller[8], the

cooling water[9] and the powder were listed in table 1. This roller was converted into a finite

element mesh with commercially available ABAQUS software as shown in Fig. 2. The calculation

was carried out by using the 8 node diffusive heat transfer elements (DCAX8R) for the heat transfer

analysis.

Results and discussion

Fig. 3 shows the temperature variation measured at the roll surface during rolling compared with the

FEM simulation and the analytic solution. As the time increases, the temperature at the roll surface

calculated by the FEM and the analytic solution gradually increases with the fluctuation due to the

contact between the hot powder and the roller surface. It can be observed that the measured

temperature is in good agreement with the FEM calculation and the analytic solution. In case of the

cooling

heatnux due to

compacting powder

h,

Fig. 1 Schematic diagram of

hot pressing roller Fig. 2 Finite element mesh for the simulation

m,-~~~~~~~~

"'

OLO ~000..,...._,1..,..,-_...,...._,_3000,.._._,...,...~_-....,'-_,-J_

llmt(ooc)

(a)

ar-~--~~--~~--, ...

D 12DOtiDOMI0300031D0 Tl<re(sec)

(b)

Fig. 3 Surface temperature results by experiment, FEM

and analytic model (a) PM1 and (b) PM2

~.-~~~~~~~~~

%71

.. o a 1200 1100 3400 3000 sao 4200 4110:) 11400

llmt(MC)

Fig. 4 Surface temperature results

by the analytic without Fe and FEM

for PM1 powder

3230 PRICM-5

rolling ofPMl, the mean surface temperature comes to almost about 230 t; as shown in Fig. 3 (a).

As for the rolling of PM2 which has the larger h5, the mean surface temperature at the steady state,

which is about 43o ·c, is higher than that ofPMl as shown in Fig. 3 (b).

Fig. 4 shows that the temperature calculated by the analytic solution without the correction factor

(Fe) is a little bit higher than the results by the FEM. As the calculation was based on spherical

coordinate system, the surface area was evaluated larger than that in our roll system. Therefore

more heat flux would penetrate into the roller and this causes the higher surface temperature.

SKT4 roller Cooling water Powder

r. o.600 m D 0.02 m PM! PM2 (course) (fine)

r, 0.420m P w 0.9950 Kglm3 a 0.10 BlDl 0.0285 1111

p 7840 Kglm3 Uw 8.38 m/sec b 2.00 1111 0.5700 mm

CP 460 J/Kg 'C Cp.w 4178 JIKg'C kh 36 Wlm 'C 36 Wlm 'C

k 36 W/m'C kw 620 X 10·3 w /m'C h, 550 W/m2 'C 1900W/m2 'C

a 9.982 X 10·6 m2/sec ll w 7.69 X 10-6 Nseclm2 TP 700'C 700 'C

v 0.3 Tc 35 'C

E 210GPa he 26300 W/m' 'C

Table 1 Size and material properties [8, 9]

Summary

The suggested analytic model, which can calculate non steady state heat transfer of the hot pressing

roller, was verified with the FEM and the experimental results. The result by the analytic model

gave a reasonable prediction that the temperature at roll surface gradually increases with the

fluctuation as the time increase compared with the FEM and the experiment. The powder size effect

is one of the most important factors for temperature on roller surface because it induced the surface

contact heat transfer coefficient.

REFERENCES

[1] T. Hirohata, S. Masaki and S. Shima: J. Mater. Proc. Techn. Vol. 111 (200l),p. 113

[2] R.T. Dec, A. Zavaliangos and J.C. Cunningham : Powder Technology Vol. 130 (2003),p. 265

[3] Sang Woo Choi and Young Seog Lee: Metals and Materials Int. Vol8 (2002), p. 25

[4] W.H.Acadams : Heat Transmission. 3rd ed. (McGraw-Hill1954).

[5] A. Degiovanni ~md C. Moyne : Rev. Generate Thermique Vol. 28 (1989),p. 557

[6] J.J. Saigon, F. Robbe-Valloire, J. Blouet and J. Bransier : Int. J. Heat Mass Transfer. Vol. 40

(1997),p. 1121

[7] M. Ozisik : Heat Conduction (John Wiley & Sons 1980).

[8] Hyung-Jun Chang and Kyu Hwan Oh, POSCO project report ( POSCO 2003).

[9] Frank P. Incropera and David P. Dewitt, Introduction to heat transfer (Wiley 1990).